Definable groups in models of Presburger Arithmetic and G^{00}

Alf Onshuus; Mariana Vicaría

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arXiv · 1612.09042

Definable groups in models of Presburger Arithmetic and G^{00}

Alf Onshuus·Mariana Vicaría

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Abstract

This paper is devoted to understand groups definable in Presburger arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic is abelian-by-finite. Theorem 2. Every bounded group definable in a model (Z,+,<) of Presburger Arithmetic is definably isomorphic to (Z, +)^{n} mod out by a lattice.

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BibTeX RIS

Alf Onshuus, Mariana Vicaría. 2016-12-29. Definable groups in models of Presburger Arithmetic and G^{00}. https://arxiv.org/abs/1612.09042

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